物理化学傅献彩版知识归纳

···································································································1···············································································3···············································································5········································8·····························································································11·························································································12·············································································14·····················································································16·························································18·····················································································20·····························································21·····························································22·············································································24·····················································2511.pVnRT=mpVRTM=pRTMρ=2.5Boyle-Marriote1122pVpV=Charles-Gat-Lussac1212VVTT=AvogadroDaltoniiinRTppxV==AmagatiiinRTVVxp==3.1.522d4expd22vNmmvvvNkTkTπ⎛⎞⎛⎞=−⎜⎟⎜⎟⎝⎠⎝⎠~(d)vvv+1.51.5d21expdENEEENkTkTπ⎛⎞⎛⎞=−⎜⎟⎜⎟⎝⎠⎝⎠~(d)EEE+11expENENkT→∞⎛⎞=−⎜⎟⎝⎠1E2121expEENEENkT→∞→∞−⎛⎞=−⎜⎟⎝⎠2E1Em22kTRTvmM==a88kTRTvmMππ==233kTRTumM==mM1kg4.2a'zvdnπ=2a'2zvdnπ=2222a12'222RTznzdnvndMπππ===28ABABRTzdnnππµ=5.ABBAvMvM=6.vanderwaals()m2mapVbRTV⎛⎞+−=⎜⎟⎝⎠m,ccc2832727aaVbTpRbb===7.vanderwaals()23318πβτβ⎛⎞+−=⎜⎟⎝⎠8.mpVpVZRTnRT==1Z1Z31.UQW∆=+dUQWδδ=+eddUQpVδ=−2.HUpV=+dVVVQUCTTδ∂⎛⎞==⎜⎟∂⎝⎠dpppQHCTTδ∂⎛⎞==⎜⎟∂⎝⎠pVCCnR−=3.WQU∆H∆WQU∆H∆000021lnVnRTV−21lnVnRTV00021dTVTCT∫21dTVTCT∫21dTpTCT∫epV−∆QUW=∆−21dTVTCT∫21dTpTCT∫21dTVTCT∫22111pVpVγ−−021dTVTCT∫21dTpTCT∫21()1nRTTδ−−QUW=∆−21dTVTCT∫21dTpTCT∫44.-1pHTTHpCpµ⎛⎞⎛⎞∂∂==−⎜⎟⎜⎟∂∂⎝⎠⎝⎠5.pQH=∆VQU=∆()gpVQQnRT−=∆rmfm()BBHHBυ∆=∆∑\\rmcm()BBHHBυ∆=−∆∑\\6.21rm2rm1r()()dTpTHTHTCT∆=∆+∆∫51.hWQη=ch1TTη=−Carnotirrηη≤2.ClausiusBAB=A0iiiQSTδ→∆−≥∑3.HelmholtzGibbsAUTS=−GHTSUpVTSApV=−=+−=+4.d0S≥Helmholtzd0A≤Gibbsd0G≤5.MaxwelldddUTSpV=−VUTS∂⎛⎞=⎜⎟∂⎝⎠TUpV∂⎛⎞=−⎜⎟∂⎝⎠SVTpVS∂∂⎛⎞⎛⎞=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠dddHTSVp=+pHTS∂⎛⎞=⎜⎟∂⎝⎠SHVp⎛⎞∂=⎜⎟∂⎝⎠pSTVpS⎛⎞∂∂⎛⎞=⎜⎟⎜⎟∂∂⎝⎠⎝⎠dddASTpV=−−VAST∂⎛⎞=−⎜⎟∂⎝⎠TApV∂⎛⎞=−⎜⎟∂⎝⎠TVSpVT∂∂⎛⎞⎛⎞=⎜⎟⎜⎟∂∂⎝⎠⎝⎠dddGSTVp=−+pGST∂⎛⎞=−⎜⎟∂⎝⎠TGVp⎛⎞∂=⎜⎟∂⎝⎠pTSVpT⎛⎞∂∂⎛⎞=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠6.Gibbs-Helmholtz62pGHTTT⎡∆⎤⎛⎞∂⎜⎟⎢⎥∆⎝⎠⎢⎥=−∂⎢⎥⎢⎥⎣⎦2pAUTTT⎡∆⎤⎛⎞∂⎜⎟⎢⎥∆⎝⎠⎢⎥=−∂⎢⎥⎢⎥⎣⎦7.,,SAG∆∆∆∆S1pVTVmr,rnCddddTpVUWTQTTSδδ−==−=22,m1121,m12lnlnlnlnVpTVSnCnRTVTpnCnRTp∆=+=+2112lnlnVpSnRnRVp∆==2,m1lnVTSnCT∆=2,m1lnpTSnCT∆=2,mdVnCSTT∆=∫3,mdpnCSTT∆=∫4/SHT∆=∆5//SQTQT∆==−61267rmmBBSSν∆=∑\\G∆10G∆=2GHTS∆=∆−∆3()()2211GHTSHTSTS∆=∆−∆=∆−−G∆A∆10A∆=72()AUTSGpV∆=∆−∆=∆−∆3()()2211AUTSUTSTS∆=∆−∆=∆−−A∆81./BBxnn=/BBAmnW=/BBcnV=/BBWWω=BA2.,,CBBTpnZZn∂⎛⎞=⎜⎟∂⎝⎠1kBBBZnZ==∑BBBHUpVHUpV=+⇒=+BBBAUTSAUTS=−⇒=−BBBGHTSGHTS=−⇒=−BBTTGGVVpp∂∂⎛⎞⎛⎞=⇒=⎜⎟⎜⎟∂∂⎝⎠⎝⎠BBppGGSSTT∂∂⎛⎞⎛⎞=−⇒=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠,,CCBBppnTTnSVSVpTpT⎛⎞⎛⎞∂∂∂∂⎛⎞⎛⎞=−⇒=−⎜⎟⎜⎟⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠⎝⎠⎝⎠3.,,,,,,,,CCCCBBBBBTpnSVnSpnTVnGUHAnnnnµ∂∂∂∂⎛⎞⎛⎞⎛⎞⎛⎞====⎜⎟⎜⎟⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠⎝⎠⎝⎠4.9ddddddddddddddddBBBBBBBBBBBBUTSpVnHTSVpnASTpVnGSTVpnµµµµ=−+=++=−−+=−−+∑∑∑∑5.Raoult*AAAppx=HenryBxBmBcBpkxkmkc===6.(,)()ln(/)TpTRTppµµ=+\\(,)()ln(/)TpTRTfpµµ=+\\*(,)()ln(/)(,)lnBBBBTpTRTppTpRTxµµµ=+=+\\*(,)(,)lnBBBTpTpRTxµµ=+*,m(,)()dpBBpTpTVpµµ=+∫\\*(,)(,)lnAAATpTpRTxµµ=+**(,)(,)ln(,)()ln(/)(,)ln(,)()ln(/)(,)ln(,)()ln(/)BBBBxBBBmBBBcTpTpRTxTpTRTkpmTpRTTpTRTkmpmcTpRTTpTRTkcpcµµµµµµµµµµ=+=+=+=+=+=+.V\\\\\\\\\\*(,)(,)lnAAAAAATpTpRTaaxµµγ=+=*,,,,,,,,,(,)(,)ln(,)ln/(,)ln/BBBxBxBxBBmBmBmBBBcBcBcBTpTpRTaaxTpRTaammTpRTaaccµµγµγµγ=+==+==+=.\\7.()2ff*ffus()BmBARTAKmnTHn==⋅∆∆10()2*bbvbapb()AmBTRTKMHAKm∆=⋅∆=BVnRTΠ=8.Gibbs-Duhemd0BBBnµ=∑Duhem-Marfulelnln0ABABABTTppxxxx∂∂⎛⎞⎛⎞−=⎜⎟⎜⎟∂∂⎝⎠⎝⎠9.BBckcαβ=111.'CSRR=−−SRR’2.2fCΦ=−+2fCΦn=−+*1fCΦ=−+123.1C=23fCΦΦ=−+=−03124.2C=24fCΦΦ=−+=−0413px−Tx−5.3C=25fCΦΦ=−+=−0514.121.rmrmflnGGRTQ∆=∆+\rmflnGRTK∆=−\\2.()f/BBBKfpυ=∏\\afpKKK==\\\()ppBKKpυ∑=\\xpBpKKpυ−∑⎛⎞=⎜⎟⎝⎠\\cpBRTKKpυ−∑⎛⎞=⎜⎟⎝⎠\\ppKKKγ=\\3.Jibbsrm,BBBTpGGυµξ∂⎛⎞∆==⎜⎟∂⎝⎠∑4.rm0BBBGυµ∆=∑rm0BBBGυµ∆==∑rm0BBBGυµ∆=∑5.rm2dlndHKTRT∆=\\rm0H∆\dln0dKT\K\136.*xmlnpKVpRT∂∆⎛⎞=⎜⎟∂⎝⎠pKcKxK0BBυ∑7.0BBυ∑0BBυ∑141.2.(),,UVNΩ1pΩ=xΩxpΩΩ=3.BoltzmanlnSkΩ=4.Boltzmann/*/ijkTiikTjjgeNNgeεε−−=∑5./ikTiiqgeε−=∑trvenqqqqqq=⋅⋅⋅⋅lnNAkTq=−ln!NqAkTN=−,lnlnNVNqSkqNkTT∂⎛⎞=+⎜⎟∂⎝⎠,lnln!NVNqqSkNkTNT∂⎛⎞=+⎜⎟∂⎝⎠,lnlnNTNqGkTqNkTVV∂⎛⎞=+⎜⎟∂⎝⎠,lnln!NTNqqGkTNkTVNV∂⎛⎞=+⎜⎟∂⎝⎠2,lnVNqUNkTT∂⎛⎞=⎜⎟∂⎝⎠152,,lnlnVNTNqqHNkTNkTVTV∂∂⎛⎞⎛⎞=+⎜⎟⎜⎟∂∂⎝⎠⎝⎠,lnTNqpNkTV∂⎛⎞=⎜⎟∂⎝⎠2,lnVVNVqCNkTTT∂⎡∂⎤⎛⎞=⎜⎟⎢⎥∂∂⎝⎠⎣⎦6.Bose-Einstein1iiigNeαβε−−=−7.Femi-Dirac1iiigNeαβε−−=+161.QznF=2.iiiiijjjjQnzrtQnzr==∑1ittt+−=+=∑∑∑3.RΩGS1−Ω1AGRlκ==4.1m1m21Sm−⋅5.mcκΛ=6.mm(1)cΛΛβ∞=−7.mm,+m,Λνλνλ∞∞∞+−−=+8.MAMAzzνννν+−+−+−→+()lnBBBTRTaµµ=+\Bµνµνµ++−−=+Bµνµνµ++−−=+\\\()lnTRTaµµ+++=+\()lnTRTaµµ−−−=+\Baaaνν+−+−=⋅17()1/aaaννν+−±+−=⋅()1/νννγγγ+−±+−=⋅()1/mmmννν+−±+−=⋅9.212iiiImz=∑10.-lgAzzIγ±+−=−1811221233NestC+DG+Hcdgh→GHCDlnlnBghBcdBaaRTRTEEEazFaazFν=−=−∏\\4lnRTEKzF=\\5rH∆rS∆rQrmpEHzEFzFTT∂⎛⎞∆=−+⎜⎟∂⎝⎠rmpESzFT∂⎛⎞∆=⎜⎟∂⎝⎠rrmpEQTSzFTT∂⎛⎞=∆=⎜⎟∂⎝⎠6lnaRTzFaϕϕ=−\71EE\pET∂⎛⎞⎜⎟∂⎝⎠19rmG∆